Active regenerative chatter suppression during boring manufacturing process

Machining performance such as that of the boring process is often limited by chatter vibration at the tool–workpiece interface. Among various sources of chatter, regenerative chatter in cutting systems is found to be the most detrimental. It limits cutting depth (as a result, productivity), adversely affects surface finish and causes premature tool failure. Though the machining system is a distributed system, all current active controllers have been designed based upon a simplified lumped single degree of freedom cutting process model. This is because it was found that in the majority of cutting processes, there exists only one dominating mode. However, such simplification does have some potential problems. First, since the system itself is a distributed system, theoretically it consists of infinite number of vibration modes. When the controller is designed to control the dominating mode(s) only, the energy designed to suppress the particular mode(s) may excite the rest of the structural modes, which unavoidably causes the so-called spillover problem. Second, the success of the control design of such simplified single degree of freedom system relies on the availability of accurate model parameters (such as the effective mass, stiffness and damping), which is unfortunately very hard to acquire. This is because the global properties are varying with the metal removal process and the movable components of machine tool. In this paper, an active controller designed from wave point of view is used to absorb chatter vibration energy in a broad frequency band to improve machining performance of a non-rotating boring bar. In contrast to most of the current active chatter control design, the wave controller is designed based on the real distributed cutting system model. The main advantage of such a control scheme to chatter suppression is its robustness to model uncertainties. The control scheme also eliminates the control spillover problem.     

Minimizing control variation in nonlinear optimal control

In any real system, changing the control signal from one value to another will usually cause wear and tear on the system’s actuators. Thus, when designing a control law, it is important to consider not just predicted system performance, but also the cost associated with changing the control action. This latter cost is almost always ignored in the optimal control literature. In this paper, we consider a class of optimal control problems in which the variation of the control signal is explicitly penalized in the cost function. We develop an effective computational method, based on the control parameterization approach and a novel transformation procedure, for solving this class of optimal control problems. We then apply our method to three example problems in fisheries, train control, and chemical engineering.     

A switching robust model predictive control approach for nonlinear systems

This work considers enhancing the stability and improving the economic performance of nonlinear model predictive control in the presence of disturbances or model uncertainties. First, a robust control Lyapunov function (RCLF)-based predictive control strategy is proposed. Second, the approximate dynamic programming (ADP) is employed to further improve regulation performance. Finally, the ADP and RCLF-MPC are combined to provide a switching control scheme, which is illustrated on a CSTR example to show its effectiveness.     

On robust regulation via sliding mode for nonlinear systems

A robust control scheme for the output tracking of nonlinear systems is proposed. The scheme is based on the nonlinear regulator theory and the sliding mode approach. It is shown that if perturbations and/or uncertainties appear on the system, the sliding mode controller is able to perform approximate asymptotic tracking, in the sense that the output tracking error remains bounded, provided the upper bounds of the uncertain terms are known.     

On robust stability of discrete-time adaptive nonlinear control

We consider adaptive control of discrete-time nonlinear systems with a single unknown parameter in this paper. We demonstrate that the necessary and sufficient condition for the existence of a feedback stabilizer that is robust to bounded noise is that the nonlinear growth rate of the system dynamics is less than 4. This result further confirms the conclusion of Guo [On critical stability of discrete-time adaptive nonlinear control, IEEE Trans. Automat. Control 42 (1997) 1488–1499] which addresses unbounded noise in a stochastic setting. Also in our worst-case approach, we find that much simpler adaptive stabilizers can be constructed when the nonlinear growth rate is less than 4.     

具有输入齿隙的一类非线性不确定系统自适应鲁棒控制

针对一类具有未知输入齿隙、参数不确定以及未建模动态和干扰的非线性系统,设计了自适应鲁棒控制器.将齿隙非线性模型等价表示为具有有界建模误差的全局线性化模型,在此基础上设计了包含自适应模型补偿、反馈稳定和鲁棒反馈3部分的自适应鲁棒控制器,并给出了系统动态跟踪误差和稳态误差指标.理论分析证明,闭环控制系统信号有界且跟踪误差在任意期望的精度范围内,仿真研究验证了所提出方法的有效性.     

On the optimal control of nonlinear systems

The Lie algebra of tensors on a Hilbert space is used to obtain optimal controls for a class of nonlinear systems.     

Open-loop and closed-loop robust optimal control of batch processes using distributional and worst-case analysis

The recognition that optimal control trajectories for batch processes can be highly sensitive to model uncertainties has motivated the development of methods for explicitly addressing robustness during batch processes. This study explores the incorporation of robust performance analysis into open-loop and closed-loop optimal control design. Several types of robust performance objectives are investigated that incorporate worst-case or distributional robustness metrics for improving the robustness of batch control laws, where the distributional approach computes the distribution of the performance index caused by parameter uncertainty. The techniques are demonstrated on a batch crystallization process. A comprehensive comparison of the robust performance of the open-loop and closed-loop system is provided.     

Asymptotic optimal control of uncertain nonlinear Euler–Lagrange systems

A sufficient condition to solve an optimal control problem is to solve the Hamilton–Jacobi–Bellman (HJB) equation. However, finding a value function that satisfies the HJB equation for a nonlinear system is challenging. For an optimal control problem when a cost function is provided a priori, previous efforts have utilized feedback linearization methods which assume exact model knowledge, or have developed neural network (NN) approximations of the HJB value function. The result in this paper uses the implicit learning capabilities of the RISE control structure to learn the dynamics asymptotically. Specifically, a Lyapunov stability analysis is performed to show that the RISE feedback term asymptotically identifies the unknown dynamics, yielding semi-global asymptotic tracking. In addition, it is shown that the system converges to a state space system that has a quadratic performance index which has been optimized by an additional control element. An extension is included to illustrate how a NN can be combined with the previous results. Experimental results are given to demonstrate the proposed controllers.     

A tool to analyze robust stability for constrained nonlinear MPC

A sufficient condition for robust asymptotic stability of nonlinear constrained model predictive control (MPC) is derived with respect to plant/model mismatch. This work is an extension of a previous study on the unconstrained nonlinear MPC problem, and is based on nonlinear programming sensitivity concepts. It addresses the discrete time state feedback problem with all states measured. A strategy to estimate bounds on the plant/model mismatch is proposed that can be used off-line as a tool to assess the extent of model mismatch that can be tolerated to guarantee robust stability.     

Fuzzy adaptive backstepping robust control for SISO nonlinear system with dynamic uncertainties

In this paper, a fuzzy adaptive backstepping design procedure is proposed for a class of nonlinear systems with three types of uncertainties: (i) nonlinear uncertainties; (ii) unmodeled dynamics and (iii) dynamic disturbances. The fuzzy logic systems are used to approximate the nonlinear uncertainties, nonlinear damping terms are used to counteract the dynamic disturbances and fuzzy approximation errors, and a dynamic signal is introduced to dominate the unmodeled dynamics. The derived fuzzy adaptive control approach guarantees the global boundedness property for all the signals and states, and at the same time, steers the output to a small neighborhood of the origin. Simulation studies are included to illustrate the effectiveness of the proposed approach.     

非线性系统的输入多采样率模糊优化控制

基于多采样率数字控制理论,讨论了非线性连续被控对象和输入多采样率模糊控制器的设计问题.提出用线性矩阵不等式凸优化技术构建非线性系统的输入多采样率T-S模糊模型,并相应地研究了基于优化区域极点配置的PDC状态反馈控制.通过解代数Riccati方程得到控制器的参数,给出了优化数字控制器的设计算法和闭环系统的稳定性条件.计算机仿真表明了所提出方法的有效性.     

Event-triggered robust model predictive control of continuous-time nonlinear systems

The event-triggered control is of compelling features in efficiently exploiting system resources, and thus has found many applications in sensor networks, networked control systems, multi-agent systems and so on. In this paper, we study the event-triggered model predictive control (MPC) problem for continuous-time nonlinear systems subject to bounded disturbances. An event-triggered mechanism is first designed by measuring the error between the system state and its optimal prediction; the event-triggered MPC algorithm that is built upon the triggering mechanism and the dual-mode approach is then designed. The rigorous analysis of the feasibility and stability is conducted, and the sufficient conditions for ensuring the feasibility and stability are developed. We show that the feasibility of the event-triggered MPC algorithm can be guaranteed if, the prediction horizon is designed properly and the disturbances are small enough. Furthermore, it is shown that the stability is related to the prediction horizon, the disturbance bound and the triggering level, and that the state trajectory converges to a robust invariant set under the proposed conditions. Finally, a case study is provided to verify the theoretical results.     

Realization of robust nonlinear model predictive control by offline optimisation

This paper describes a new method for increasing the computational efficiency of nonlinear robust model-based predictive control. It is based on the application of neuro-fuzzy networks and improves the computation efficiency by arranging the online optimisation to be done offline. The offline optimisation is realized by offline training a neuro-fuzzy network, consisting of zero-order T–S fuzzy rules, which is designed to approximate the input–output relationship of a robust model-based predictive controller. The design and the training of the neuro-fuzzy network are described, and the corresponding control algorithm is developed. Experiment results performed on the temperature control loop of an experimental air-handling unit (AHU) demonstrate the effectiveness of this approach.     

非线性离散系统的信息融合最优预见控制

将信息融合思想引入非线性离散系统的预见控制,提出了信息融合最优预见控制,将对控制系统的所有性能要求和系统动力学转化为可融合信息;然后从信息融合估计的角度,使原问题转化为求控制量的"融合估计"问题.推导了基于卡尔曼滤波器的最优预见控制算法,讨论了预见步数的选取问题,并通过对机械手的转移控制仿真研究说明了信息融合最优预见控制算法的有效性.     

Stability margins of nonlinear receding-horizon control via inverse optimality

Using the nonlinear analog of the Fake Riccati equation developed for linear systems, we derive an inverse optimality result for several receding-horizon control schemes. This inverse optimality result unifies stability proofs and shows that receding-horizon control possesses the stability margins of optimal control laws.     

一类不确定非线性纯反馈系统的自适应鲁棒模糊控制

针对一类带有不确定性的非线性MIMO纯反馈系统,提出一种自适应鲁棒模糊控制方法,该方法放宽了已有文献对系统模型的限制条件,基于李雅普诺夫分析方法获得了控制输入和自适应律．在控制输入设计中,鲁棒控制项用于补偿逼近误差向量．通过选择适当的设计参数。提出的控制方法使得闭环系统的所有信号是一致有界的和跟踪误差向量的范数收敛到小的零邻域内．仿真结果表明了所提出方法的有效性．